Solve frac{sqrt{6}}{frac{sqrt{3}}{2}}=b/frac{1{2}sqrt{2}}

$$\frac{ \sqrt{ 6 } }{ \frac{ \sqrt{ 3 } }{ 2 } } = \frac{ b }{ \frac{ 1 }{ 2 } \sqrt{ 2 } }$$

Solve for b

$$b=2$$

Steps for Solving Linear Equation

Divide \sqrt{6} by \frac{\sqrt{3}}{2} by multiplying \sqrt{6} by the reciprocal of \frac{\sqrt{3}}{2}.

$$\frac{\sqrt{6}\times 2}{\sqrt{3}}=\frac{b}{\frac{1}{2}\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{6}\times 2}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\sqrt{6}\times 2\sqrt{3}}{\left(\sqrt{3}\right)^{2}}=\frac{b}{\frac{1}{2}\sqrt{2}}$$

The square of \sqrt{3} is 3.

$$\frac{\sqrt{6}\times 2\sqrt{3}}{3}=\frac{b}{\frac{1}{2}\sqrt{2}}$$

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

$$\frac{\sqrt{3}\sqrt{2}\times 2\sqrt{3}}{3}=\frac{b}{\frac{1}{2}\sqrt{2}}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{3\times 2\sqrt{2}}{3}=\frac{b}{\frac{1}{2}\sqrt{2}}$$

Cancel out 3 and 3.

$$2\sqrt{2}=\frac{b}{\frac{1}{2}\sqrt{2}}$$

Rationalize the denominator of \frac{b}{\frac{1}{2}\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$2\sqrt{2}=\frac{b\sqrt{2}}{\frac{1}{2}\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$2\sqrt{2}=\frac{b\sqrt{2}}{\frac{1}{2}\times 2}$$

Cancel out 2 and 2.

$$2\sqrt{2}=\frac{b\sqrt{2}}{1}$$

Anything divided by one gives itself.

$$2\sqrt{2}=b\sqrt{2}$$

Swap sides so that all variable terms are on the left hand side.

$$b\sqrt{2}=2\sqrt{2}$$

The equation is in standard form.

$$\sqrt{2}b=2\sqrt{2}$$

Divide both sides by \sqrt{2}.

$$\frac{\sqrt{2}b}{\sqrt{2}}=\frac{2\sqrt{2}}{\sqrt{2}}$$

Dividing by \sqrt{2} undoes the multiplication by \sqrt{2}.

$$b=\frac{2\sqrt{2}}{\sqrt{2}}$$

Divide 2\sqrt{2} by \sqrt{2}.

$$b=2$$